Terminally functionalized polymers are useful precursors for the preparation of polymers containing functional end groups. Examples of terminally functionalized polymers are vinylidene-terminated polyolefins. Polymers containing functional end groups have several useful purposes. For example, polyisobutylene (PIB) containing vinylidene chain ends are utilized in the synthesis of PIB-succinic anhydrides (PIBSAs), which are key intermediates in the production of PIB-based succinimide dispersants for use as additives for engine lubricants. Vinylidene-terminated PIBs are also utilized in the production of PIB-amines, which are useful as fuel additives. An opportunity exists to create polyolefins containing sulfide end groups for use in lubricant applications. These thio-terminated polyolefins can offer oxidation inhibition and surface affinity, two important factors in the design of lubricant additive technology. Thus, there is a need for new classes of terminally functionalized polymers, as well as methods of selectively or exclusively producing terminally functionalized polymers, such as vinylidene-terminate polyolefins and sulfide-terminated polyolefins.